Step 1: We add the available piece of fabrics she has, that is;
[tex]2\frac{1}{2}+4\frac{1}{4}[/tex]We can convert the mixed fraction to an improper fraction as;
[tex]\frac{5}{2}+\frac{17}{4}[/tex]Also;
[tex]\frac{5}{2}=\frac{10}{4}[/tex]Then;
[tex]\begin{gathered} \frac{5}{2}+\frac{17}{4}=\frac{10}{4}+\frac{17}{4} \\ \frac{5}{2}+\frac{17}{4}=\frac{27}{4} \end{gathered}[/tex]So, to get the remainder, we deduct from the number of yards needed to make the quilt.
[tex]10\frac{1}{2}-\frac{27}{4}[/tex]Also, we change the mixed fraction to an improper fraction, we have;
[tex]\frac{21}{2}-\frac{27}{4}[/tex]But;
[tex]\frac{21}{2}=\frac{42}{4}[/tex][tex]\begin{gathered} \frac{21}{2}-\frac{27}{4}=\frac{42}{4}-\frac{27}{4} \\ \frac{21}{2}-\frac{27}{4}=\frac{15}{4} \end{gathered}[/tex]Then, we can put the improper fraction back to mixed fraction, we have;
[tex]\frac{15}{4}=3\frac{3}{4}[/tex]CORRECT OPTION: C
Similarly,
[tex]\begin{gathered} 4-\frac{1}{4} \\ 3+1-\frac{1}{4} \\ 3+\frac{3}{4} \\ 3\frac{3}{4} \end{gathered}[/tex]OR
[tex]\begin{gathered} \frac{4}{1}-\frac{1}{4} \\ \text{The lowest common multiple of the denominator is 4;} \\ \frac{4(4)-1(1)}{4}=\frac{16-1}{4}=\frac{15}{4} \\ =3\frac{3}{4} \end{gathered}[/tex]